This fall I will be running a topics course on differential topology and vector bundles. A description of the course can be found below:
Homework: These will continue to be updated until a due date is posted
Homework 1. Due Monday, October 2.
Homework 2. Due Monday, November 20.
Lecture Notes
Week 1: Smooth manifolds
Week 2: Tangent spaces and maps
Weeks 3/4: Definition of vector bundles and examples
Week 5: Introduction to geometry of bundles
Week 6: Stiefel-Whitney classes
Week 7: Stiefel-Whitey numbers
Week 8: Universal vector bundles
Week 9: Principal G-bundles
Week 10: Associated bundles
Weeks 11/12: Fibrations & Universal G-bundles
Week 13: Classifying spaces & orientations
Weeks 14/15: Chern classes and K-theory